Mode-coupling theory: generalizations, high dimensions and microscopic dynamics

This work contains several applications of the mode-coupling theory (MCT) and is separated into three parts. In the first part we investigate the liquid-glass transition of hard spheres for dimensions d→∞ analytically and numerically up to d=800 in the framework of MCT. We find that the critical packing fraction ϕc(d) scales as d²2^(-d), which is larger than the Kauzmann packing fraction ϕK(d) found by a small-cage expansion by Parisi and Zamponi [J. Stat. Mech.: Theory Exp. 2006, P03017 (2006)]. The scaling of the critical packing fraction is different from the relation ϕc(d)∼d2^(-d) found earlier by Kirkpatrick and Wolynes [Phys. Rev. A 35, 3072 (1987)]. This is due to the fact that the k dependence of the critical collective and self nonergodicity parameters fc(k;d) and fcs(k;d) was assumed to be Gaussian in the previous theories. We show that in MCT this is not the case. Instead fc(k;d) and fcs(k;d), which become identical in the limit d→∞, converge to a non-Gaussian master function on the scale k∼d^(3/2). We find that the numerically determined value for the exponent parameter λ and therefore also the critical exponents a and b depend on the dimension d, even at the largest evaluated dimension d=800. In the second part we compare the results of a molecular-dynamics simulation of liquid Lennard-Jones argon far away from the glass transition [D. Levesque, L. Verlet, and J. Kurkijärvi, Phys. Rev. A 7, 1690 (1973)] with MCT. We show that the agreement between theory and computer simulation can be improved by taking binary collisions into account [L. Sjögren, Phys. Rev. A 22, 2866 (1980)]. We find that an empiric prefactor of the memory function of the original MCT equations leads to similar results. In the third part we derive the equations for a mode-coupling theory for the spherical components of the stress tensor. Unfortunately it turns out that they are too complex to be solved numerically.

Two-Dimensional Bin Packing Problem with Guillotine Restrictions

This thesis, after presenting recent advances obtained for the two-dimensional bin packing problem, focuses on the case where guillotine restrictions are imposed. A mathematical characterization of non-guillotine patterns is provided and the relation between the solution value of the two-dimensional problem with guillotine restrictions and the two-dimensional problem unrestricted is being studied from a worst-case perspective. Finally it presents a new heuristic algorithm, for the two-dimensional problem with guillotine restrictions, based on partial enumeration, and computationally evaluates its performance on a large set of instances from the literature. Computational experiments show that the algorithm is able to produce proven optimal solutions for a large number of problems, and gives a tight approximation of the optimum in the remaining cases.

Packing a trunk : a physically based approach with full motional freedom

Geometric packing problems may be formulated mathematically as constrained optimization problems. But finding a good solution is a challenging task. The more complicated the geometry of the container or the objects to be packed, the more complex the non-penetration constraints become. In this work we propose the use of a physics engine that simulates a system of colliding rigid bodies. It is a tool to resolve interpenetration conflicts and to optimize configurations locally. We develop an efficient and easy-to-implement physics engine that is specialized for collision detection and contact handling. In succession of the development of this engine a number of novel algorithms for distance calculation and intersection volume were designed and imple- mented, which are presented in this work. They are highly specialized to pro- vide fast responses for cuboids and triangles as input geometry whereas the concepts they are based on can easily be extended to other convex shapes. Especially noteworthy in this context is our ε-distance algorithm - a novel application that is not only very robust and fast but also compact in its im- plementation. Several state-of-the-art third party implementations are being presented and we show that our implementations beat them in runtime and robustness. The packing algorithm that lies on top of the physics engine is a Monte Carlo based approach implemented for packing cuboids into a container described by a triangle soup. We give an implementation for the SAE J1100 variant of the trunk packing problem. We compare this implementation to several established approaches and we show that it gives better results in faster time than these existing implementations.

Ascending thoracic aorta dimension and outcomes in acute type B dissection (from the International Registry of Acute Aortic Dissection [IRAD])

It is not well known if the size of the ascending thoracic aorta at presentation predicts features of presentation, management, and outcomes in patients with acute type B aortic dissection. The International Registry of Acute Aortic Dissection (IRAD) database was queried for all patients with acute type B dissection who had documentation of ascending thoracic aortic size at time of presentation. Patients were categorized according to ascending thoracic aortic diameters ≤4.0, 4.1 to 4.5, and ≥4.6 cm. Four hundred eighteen patients met inclusion criteria; 291 patients (69.6%) were men with a mean age of 63.2 ± 13.5 years. Ascending thoracic aortic diameter ≤4.0 cm was noted in 250 patients (59.8%), 4.1 to 4.5 cm in 105 patients (25.1%), and ≥4.6 cm in 63 patients (15.1%). Patients with an ascending thoracic aortic diameter ≥4.6 cm were more likely to be men (p = 0.01) and have Marfan syndrome (p <0.001) and known bicuspid aortic valve disease (p = 0.003). In patients with an ascending thoracic aorta ≥4.1 cm, there was an increased incidence of surgical intervention (p = 0.013). In those with an ascending thoracic aorta ≥4.6 cm, the root, ascending aorta, arch, and aortic valve were more often involved in surgical repair. Patients with an ascending thoracic aorta ≤4.0 were more likely to have endovascular therapy than those with larger ascending thoracic aortas (p = 0.009). There was no difference in overall mortality or cause of death. In conclusion, ascending thoracic aortic enlargement in patients with acute type B aortic dissection is common. Although its presence does not appear to predict an increased risk of mortality, it is associated with more frequent open surgical intervention that often involves replacement of the proximal aorta. Those with smaller proximal aortas are more likely to receive endovascular therapy.

C-clamp and pelvic packing for control of hemorrhage in patients with pelvic ring disruption

Exsanguinating hemorrhage is the major cause of death in patients with pelvic ring disruption.